↑

Properties

Label 30.2.e
Level $30$
Weight $2$
Character orbit 30.e
Rep. character $\chi_{30}(17,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $1$
Sturm bound $12$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 30 = 2 \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 30.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(30, [\chi])\).

Total New Old
Modular forms 20 4 16
Cusp forms 4 4 0
Eisenstein series 16 0 16

Trace form

\( 4 q - 4 q^{3} - 4 q^{6} - 4 q^{7} + O(q^{10}) \) \( 4 q - 4 q^{3} - 4 q^{6} - 4 q^{7} + 4 q^{10} + 4 q^{12} + 8 q^{15} - 4 q^{16} + 8 q^{18} + 8 q^{21} - 4 q^{22} - 16 q^{25} - 4 q^{27} - 4 q^{28} - 12 q^{30} - 8 q^{31} - 4 q^{33} - 4 q^{36} + 24 q^{37} + 8 q^{40} + 4 q^{42} + 24 q^{43} - 8 q^{45} + 16 q^{46} + 4 q^{48} - 8 q^{51} + 12 q^{55} - 16 q^{57} - 20 q^{58} - 4 q^{60} - 24 q^{61} - 4 q^{63} + 8 q^{66} - 16 q^{67} + 4 q^{70} - 8 q^{72} - 20 q^{73} + 28 q^{75} + 16 q^{76} + 28 q^{81} - 16 q^{82} + 8 q^{85} + 20 q^{87} - 4 q^{88} + 8 q^{90} + 8 q^{93} + 4 q^{96} + 12 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(30, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
30.2.e.a 30.e 15.e $4$ $0.240$ \(\Q(\zeta_{8})\) None 30.2.e.a \(0\) \(-4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)